Compact Abelian group actions on injective factors

DOI10.1016/0022-1236(92)90074-SzbMath0784.46049OpenAlexW2007109678MaRDI QIDQ1187766

Yasuyuki Kawahigashi, Masamichi Takesaki

Publication date: 23 July 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90074-s

zbMATH Keywords

type III factorscocycle conjugate1-dimensional toruscentrally ergodic actionsclassification of compact Abelian group actions on injective factorsdual invariantinfinite fixed point algebrasTakesaki duality

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Classifications of (C^*)-algebras (46L35) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (16)

Classification of actions of discrete Kac algebras on injective factors ⋮ Approximate unitary equivalence of finite index endomorphisms of AFD factors ⋮ Characteristic invatiant of tensor product actions and actions on crossed products ⋮ COCYCLE CONJUGACY OF ONE PARAMETER AUTOMORPHISM GROUPS OF AFD FACTORS OF TYPE III ⋮ Classification of minimal actions of a compact Kac algebra with amenable dual ⋮ Compact Lie group action with the continuous Rokhlin property ⋮ Classification of outer actions of discrete amenable groupoids on injective factors ⋮ Actions of groups and quantum groups on amenable factors ⋮ On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type \(\text{III}_1\) ⋮ Classification of regular subalgebras of injective type III factors ⋮ Locally compact separable abelian group actions on factors with the Rokhlin property ⋮ The structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions ⋮ The non-commutative flow of weights on a von Neumann algebra ⋮ Classification of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III ⋮ Centrally trivial automorphisms and an analogue of Connes' \(\chi(M)\) for subfactors ⋮ Classification of actions of compact abelian groups on subfactors with index less than 4

Cites Work

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• Une classification des facteurs de type ${\rm III}$
• A $\mathrm{II}_1$ factor anti-isomorphic to itself but without involutory antiautomorphisms.

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